After the rules were tightened in 2014 many of these borrowers were no longer able to pass the eligibility tests of their existing lenders and some subsequently slipped onto expensive standard variable rates.

To make matters worse, the watchdog estimates that around 20,000 of these customers are stuck with lenders that are no longer active - with a further 120,000 stuck with firms that aren't regulated by the FCA.

How has the mortgage sector reacted?

Mark Harris, chief executive of mortgage broker SPF Private Clients, said: ‘It has never made sense that borrowers are prevented from switching to cheaper mortgage deals because they do not meet their lender’s affordability criteria.

'Clearly they will be better able to make mortgage payments on a cheaper rate, avoiding missing repayments and getting into debt, which will only exacerbate their situation.

'This issue has caused extreme hardship in some cases.'

Robert Sinclair, chief executive of the Association of Mortgage Intermediaries said: 'This is long overdue. It's interesting that the Tresuary Select Committee has lead the FCA to this when industry has been calling for it for years. But it's positive news.'

Nick Morrey of broker John Charcol said: 'At least the FCA is trying to open the door that will encourage lenders to allow them to take them on. But you can’t force lenders to take on bad debt.

'Of course, the subprime lenders could be rubbing their hands with glee. In terms a of time-frame, I’d like to see something happen before the end of the year.'

'To help these customers, we will consult on the changes to our responsible lending rules, with the aim to deliver a more proportionate affordability assessment.

'We intend to move the assessment from an absolute test to a relative test, thus the test would be whether the new mortgage costs are more affordable than the current mortgage costs.

'Our focus will be on those customers who are seeking to move to a cheaper mortgage and are not borrowing more.'

In simple terms, this means if a customer has been keeping up with repayments they should be able to switch to a cheaper rate regardless of whether they meet the FCA's tightened affordability criteria.

Bailey added in his letter that there needs to be a 'willingness' from industry to offer remortgaging opportunities to customers once regulatory barriers are removed.

He added that last week the FCA held a meeting with industry figures to discuss lending to customers with closed or inactive firms, stating there was a 'willingness to consider remortgage options' once rules are relaxed.

The move comes after Nicky Morgan called for more action to be taken to help mortgage prisoners stuck with inactive firms in November.

The FCA will release a consultation paper this spring, meaning it could still be some time before any actual changes are brought in.